计量地理实验报告

PAGEPAGE2计量地理学实验报告班级：地理092学号：2009011134组别：姓名：郑德欣山东建筑大学土木工程学院二零一一年十一月实验须知实验是配合课堂教学的一个重要教学环节，同时也是培养学生掌握实验的基本技能和进行基本训练的一个主要手段，为了保证实验的顺利进行，必须注意下列事项：1、实验之前，希望同学们要预习实验指导书，了解本次实验的目的，原理和要求：2、严格按操作步骤认真操作，实验报告要客观、详细记录实验步骤，实验成果等。3、爱护实验仪器，非本次实验用的仪器或虽是本次实验所用的仪器，但在老师没有讲解之前都不得随便乱动，以免损坏仪器；4、实验中不慎损坏仪器或丢失仪器中的附件，均应主动地告诉老师，按照有关规定处理；目录实验一地理数据统计处理………1实验二统计分析方法……………3实验三线性规划方法……………4实验四决策分析方法…………5实验一地理数据统计处理一、实验目的1.熟悉matlab的基本操作。2．掌握matlab的矩阵运算。3．掌握matlab计算地理数据一般水平的各个指标、离散水平的各个指标、偏离程度的各个指标4．掌握matlab的基本统计作图。二、实验内容1.熟悉matlab环境，并进行基本的矩阵运算。2.计算平均值、分组平均值、中位数、分组中位数、众数。3.计算极差、离差、离差平方和、方差与标准差、变异系数。4.计算标准偏度系数、标准峰度系数。5．进行统计作图。三、实验方法与步骤打开matlab，重点熟悉命令窗口、工作空间窗口、历史命令窗口、当前工作目录窗口的使用。运用help命令查询基本的矩阵运算函数，明确各个参数的含义，以及函数的使用和输出的结果，并代入数据进行运算。3.运用help命令查询平均值、中位数、众数的计算函数的使用方法，并将Excel表格中的数据转化成matlab数据，进行计算并分析。4.运用help命令查询极差、离差、离差平方和、方差与标准差的计算函数的使用方法，并将Excel表格中的数据转化成matlab数据，进行计算并分析。5.运用已有函数，计算分组平均值、分组中位数、变异系数。6.运用help命令查询计算标准偏度系数、标准峰度系数的计算函数的使用方法，并将Excel表格中的数据转化成matlab数据，进行计算并分析。7.运用matlab函数进行统计作图。四、结果分析1.TABULATE（频数/频率/众数）TABULATEFrequencytable.TABLE=TABULATE(X)takesavectorXandreturnsamatrix,TABLE.ThefirstcolumnofTABLEcontainstheuniquevaluesofX.Thesecondisthenumberofinstancesofeachvalue.Thelastcolumncontainsthepercentageofeachvalue.x=[2:0.1:6]x=Columns1through62.00002.10002.20002.30002.40002.5000Columns7through122.60002.70002.80002.90003.00003.1000Columns13through183.20003.30003.40003.50003.60003.7000Columns19through243.80003.90004.00004.10004.20004.3000Columns25through304.40004.50004.60004.70004.80004.9000Columns31through365.00005.10005.20005.30005.40005.5000Columns37through415.60005.70005.80005.90006.0000>>table=tabulate(x)table=2.00001.00002.43902.10001.00002.43902.20001.00002.43902.30001.00002.43902.40001.00002.43902.50001.00002.43902.60001.00002.43902.70001.00002.43902.80001.00002.43902.90001.00002.43903.00001.00002.43903.10001.00002.43903.20001.00002.43903.30001.00002.43903.40001.00002.43903.50001.00002.43903.60001.00002.43903.70001.00002.43903.80001.00002.43903.90001.00002.43904.00001.00002.43904.10001.00002.43904.20001.00002.43904.30001.00002.43904.40001.00002.43904.50001.00002.43904.60001.00002.43904.70001.00002.43904.80001.00002.43904.90001.00002.43905.00001.00002.43905.10001.00002.43905.20001.00002.43905.30001.00002.43905.40001.00002.43905.50001.00002.43905.60001.00002.43905.70001.00002.43905.80001.00002.43905.90001.00002.43906.00001.00002.43902.MEAN（平均值）MEANAverageormeanvalue.Forvectors,MEAN(X)isthemeanvalueoftheelementsinX.Formatrices,MEAN(X)isarowvectorcontainingthemeanvalueofeachcolumn.ForN-Darrays,MEAN(X)isthemeanvalueoftheelementsalongthefirstnon-singletondimensionofX.>>mean(x)ans=43.MEDIAN（中位数）MEDIANMedianvalue.Forvectors,MEDIAN(X)isthemedianvalueoftheelementsinX.Formatrices,MEDIAN(X)isarowvectorcontainingthemedianvalueofeachcolumn.ForN-Darrays,MEDIAN(X)isthemedianvalueoftheelementsalongthefirstnon-singletondimensionofX.>>median(x)ans=44.RANGE（极差）RANGESamplerange.Y=RANGE(X)returnstherangeofthevaluesinX.Foravectorinput,Yisthedifferencebetweenthemaximumandminimumvalues.Foramatrixinput,Yisavectorcontainingtherangeforeachcolumn.ForN-Darrays,RANGEoperatesalongthefirstnon-singletondimension.>>Y=range(x)Y=45.VARVariance.（方差）VARVariance.Forvectors,Y=VAR(X)returnsthevarianceofthevaluesinX.Formatrices,YisarowvectorcontainingthevarianceofeachcolumnofX.ForN-Darrays,VARoperatesalongthefirstnon-singletondimensionofX.>>y=var(x)y=1.43506.STDStandarddeviation.（标准差）STDStandarddeviation.Forvectors,Y=STD(X)returnsthestandarddeviation.Formatrices,Yisarowvectorcontainingthestandarddeviationofeachcolumn.ForN-Darrays,STDoperatesalongthefirstnon-singletondimensionofX.>>M=std(x)M=1.19797.SKEWNESSSkewness.（偏度系数）SKEWNESSSkewness.S=SKEWNESS(X)returnsthesampleskewnessofthevaluesinX.Foravectorinput,SisthethirdcentralmomentofX,dividedbythecubeofitsstandarddeviation.Foramatrixinput,SisarowvectorcontainingthesampleskewnessofeachcolumnofX.ForN-Darrays,SKEWNESSoperatesalongthefirstnon-singletondimension.>>S=skewness(x)S=-7.8465e-0178.KURTOSISKurtosis（峰度系数）.KURTOSISKurtosis.K=KURTOSIS(X)returnsthesamplekurtosisofthevaluesinX.Foravectorinput,KisthefourthcentralmomentofX,dividedbyfourthpowerofitsstandarddeviation.Foramatrixinput,KisarowvectorcontainingthesamplekurtosisofeachcolumnofX.ForN-Darrays,KURTOSISoperatesalongthefirstnon-singletondimension.>>K=kurtosis(x)K=1.7986实验二统计分析方法一、实验目的1.掌握相关分析的计算方法和计算函数。2．掌握回归分析的计算方法和计算函数。3．掌握时间序列分析的方法和编程。4．掌握系统聚类分析的计算方法和计算函数。5．掌握主成分分析的计算方法和计算函数。6．掌握马尔可夫预测的方法和编程。7．掌握趋势面分析的计算方法和计算函数。8．掌握各种统计分析方法的结果检验。二、实验内容1.运用corrcoef函数进行相关分析，并分析计算结果。2．运用regress函数进行回归分析，并进行检验。3．运用matlab编程实现移动平均、滑动平均、二次指数平滑、线性自回归。4．运用zscore、pdist、linkage、dendrogram等函数进行系统聚类分析，并分析计算结果。5．运用princomp函数进行主成分分析，并分析计算结果。6．运用matlab编程实现马尔可夫预测方法。7．运用regress函数进行趋势面分析，并进行检验。三、实验方法与步骤（一）相关分析1.运用help命令查询corrcoef函数的使用方法。2.将Excel变量数据转化成matlab数据矩阵A，调用命令：R=corrcoef(A)，计算各变量之间的相关系数矩阵。3.分析计算结果。（二）回归分析1.运用help命令查询regress函数的使用方法。2.将Excel变量数据转化成matlab数据矩阵A。3.作出散点图。4．运用[b,bint,r,rint,stats]=regress(y,x)进行计算，其中b是回归方程中的参数估计值，bint是b的置信区间，r和rint分别表示残差及残差对应的置信区间。stats包含三个数字，分别是相关系数，F统计量及对应的概率p值。5.进行检验并分析计算结果。（三）时间序列分析1.将Excel变量数据转化成matlab数据矩阵。2．编程计算移动平均、滑动平均、二次指数平滑、线性自回归。3．分析计算结果。（四）系统聚类分析1.将Excel变量数据转化成matlab数据矩阵。2．进行标准化处理。3．计算距离。4．用linkage进行聚类分析。5．做出聚类谱系图。（五）主成分分析1.运用help命令查询primcomp函数的使用方法。2.将Excel变量数据转化成matlab数据矩阵。3.运用[pc,score,latent,t2]=princomp(X)进行计算，其中①pc主分量fi的系数，也叫因子系数；注意：pcTpc=单位阵。②score是主分量下的得分值；得分矩阵与数据矩阵X的阶数是一致的。③latent是score对应列的方差向量，即A的特征值；容易计算方差所占的百分比。④t2表示检验的t2-统计量（方差分析要用）4.分析计算结果。（六）马尔可夫预测1.将Excel变量数据转化成matlab数据矩阵。2．编程进行马尔可夫预测。3．分析计算结果。（七）趋势面分析1.将Excel变量数据转化成matlab数据矩阵。2．进行矩阵计算和变换，化为二次、三次趋势面分析的原始数据矩阵。3．运用regress进行计算。4．检验计算结果。5．作出趋势面图：首先准备数据；然后运用meshgrid进行变换；最后用mesh或surf等函数做图。四、结果分析（一）相关分析CORRCOEFCorrelationcoefficients.R=CORRCOEF(X)calculatesamatrixRofcorrelationcoefficientsforanarrayX,inwhicheachrowisanobservationandeachcolumnisavariable.表格转置：>>q=[3.80 4.00 5.80 8.00 11.30 14.40 16.50 16.20 13.80 10.80 6.70 4.70]q=Columns1through83.80004.00005.80008.000011.300014.400016.500016.2000Columns9through1213.800010.80006.70004.7000>>j=[77.70 51.20 60.10 54.10 55.40 56.80 45.00 55.30 67.50 73.30 76.60 79.60]j=Columns1through877.700051.200060.100054.100055.400056.800045.000055.3000Columns9through1267.500073.300076.600079.6000>>h=[q',j']h=3.800077.70004.000051.20005.800060.10008.000054.100011.300055.400014.400056.800016.500045.000016.200055.300013.800067.500010.800073.30006.700076.60004.700079.6000>>r=corrcoef(h)r=1.0000-0.4895-0.48951.0000>>[R,P]=CORRCOEF(h)Warning:FunctioncallCORRCOEFinvokesinexactmatchD:\matlab7\toolbox\matlab\datafun\corrcoef.m.R=1.0000-0.4895-0.48951.0000P=1.00000.10630.10631.0000因为p=0.1063〉0.05所以不满足条件（二）回归分析REGRESSMultiplelinearregressionusingleastsquares.B=REGRESS(Y,X)returnsthevectorBofregressioncoefficientsinthelinearmodelY=X*B.Xisann-by-pdesignmatrix,withrowscorrespondingtoobservationsandcolumnstopredictorvariables.Yisann-by-1vectorofresponseobservations.>>y=[48.25193.72413.94……786.75584.89574.00]y=48.2500193.7200413.9400……786.7500584.8900574.0000>>x1=[40.5036.6035.53……34.2135.4336.14]x1=40.500036.600035.5300……34.210035.430036.1400>>x2=[1170.801707.201908.80……3362.701221.201111.70]x2=1.0e+003*1.17081.70721.9088……3.36271.22121.1117>>[B,BINT,R,RINT,STATS]=REGRESS(y,[ones(53,1)x1x2])Warning:FunctioncallREGRESSinvokesinexactmatchD:\matlab7\toolbox\stats\regress.m.B=1.0e+003*3.2951-0.08120.0000BINT=1.0e+003*2.88253.7078-0.0920-0.0704-0.00000.0001R=-1.7426-192.2752-66.2118……146.7975121.5216172.2303RINT=-179.3270175.8418-367.0625-17.4879-247.9691115.5456…………-16.8142310.4091-56.2909299.3340-1.9993346.4599STATS=1.0e+003*0.00080.119308.3189R2f值（三）多元非线性回归（趋势面分析）>>z=[27.638.4……44.9]z=27.600038.4000……44.9000>>x=[01.1……3.65]x=01.1000……3.6500>>y=[10.6……2.55]y=1.00000.6000……2.5500>>[B,BINT,R,RINT,STATS]=REGRESS(z,[ones(12,1)xyx.^2x.*yy.^2])B=5.998017.438229.7874-3.58830.3569-8.0695BINT=-18.528830.52480.760834.11557.440352.1346-7.22960.0530-3.58284.2966-13.1699-2.9691R=-0.11592.3589-1.7605-1.51332.31581.3295-1.45740.71832.5279-8.91778.2646-3.7500RINT=-9.16438.9324-9.980114.6978-11.75358.2324-13.027010.0005-6.880311.5119-7.29879.9577-14.333011.4181-10.463311.8998-5.898910.9546-16.4202-1.41511.302715.2265-10.04202.5420STATS=0.83866.23590.022731.5030R^2F值P值做趋势面的三维图首先对模型方程的xy赋值x=[0:0.2:4] X=X'Y=[1:0.2:5]Y=Y’Z=5.998+17.438*X+29.787*Y-3.558*X.^2+0.357*X.*Y-8.07*Y.^2在matlab中执行这个方程得到Z对应的值，然后做三维图所用的函数方法是：方法一helpmeshgridMESHGRIDXandYarraysfor3-Dplots.[X,Y]=MESHGRID(x,y)transformsthedomainspecifiedbyvectorsxandyintoarraysXandYthatcanbeusedfortheevaluationoffunctionsoftwovariablesand3-Dsurfaceplots.TherowsoftheoutputarrayXarecopiesofthevectorxandthecolumnsoftheoutputarrayYarecopiesofthevectory.[X,Y]=MESHGRID(x)isanabbreviationfor[X,Y]=MESHGRID(x,x).[X,Y,Z]=MESHGRID(x,y,z)produces3-Darraysthatcanbeusedtoevaluatefunctionsofthreevariablesand3-Dvolumetricplots.由mesh(X,Y,Z)得方法2surf(X,Y,Z)（四）系统聚类分析1.>>x=[363.912141.503100.695143.739131.41268.33795.41662.90186.62491.39476.91251.27468.83177.30176.94899.265118.505141.473137.761117.612122.781]2.回车后得到一个21*9矩阵3.>>helpzscoreZSCOREStandardizedzscore.Z=ZSCORE(X)returnsacentered,scaledversionofX,knownastheZscoresofX.Foravectorinput,Z=(X-MEAN(X))./STD(X).Foramatrixinput,ZisarowvectorcontainingtheZscoresofeachcolumnofX.ForN-Darrays,ZSCOREoperatesalongthefirstnon-singletondimension.4.输入>>z=zscore(x)得到标准差标准化的数据5.>>helppdist6.>>y=pdist(z)7.>>helplinkage8.>>z=linkage(y)z=9.000010.00000.457412.000013.00000.800617.000019.00000.933916.000024.00000.956522.000023.00000.972218.000025.00000.985215.000026.00001.048327.000028.00001.12897.000029.00001.181320.000030.00001.40676.00008.00001.480431.000032.00001.804121.000033.00001.93652.00005.00002.068711.000034.00002.14443.000014.00002.48414.000035.00002.674236.000037.00002.721338.000039.00002.88551.000040.00005.67949.>>helpdendrogram10.>>dendrogram(z)

实验三线性规划方法一、实验目的1.熟悉matlab优化工具箱。2．掌握线性规划方法。二、实验内容1.练习matlab优化工具箱的相关函数。2.运用linprog进行线性规划。三、实验方法与步骤1.运用help命令查询linprog函数的使用方法。2.建立线性规划模型。3.运用linprog进行计算四、结果分析LINPROGLinearprogramming.X=LINPROG(f,A,b)attemptstosolvethelinearprogrammingproblem:minf'*xsubjectto:A*x<=bxX=LINPROG(f,A,b,Aeq,beq)solvestheproblemabovewhileadditionallysatisfyingtheequalityconstraintsAeq*x=beq.X=LINPROG(f,A,b,Aeq,beq,LB,UB)definesasetoflowerandupperboundsonthedesignvariables,X,sothatthesolutionisintherangeLB<=X<=UB.UseemptymatricesforLBandUBifnoboundsexist.SetLB(i)=-InfifX(i)isunboundedbelow;setUB(i)=InfifX(i)isunboundedabove.X=LINPROG(f,A,b,Aeq,beq,LB,UB,X0)setsthestartingpointtoX0.Thisoptionisonlyavailablewiththeactive-setalgorithm.Thedefaultinteriorpointalgorithmwillignoreanynon-emptystartingpoint.X=LINPROG(f,A,b,Aeq,beq,LB,UB,X0,OPTIONS)minimizeswiththedefaultoptimizationparametersreplacedbyvaluesinthestructureOPTIONS,anargumentcreatedwiththeOPTIMSETfunction.SeeOPTIMSETfordetails.OptionsareDisplay,Diagnostics,TolFun,LargeScale,MaxIter.Currently,only'final'and'off'arevalidvaluesfortheparameterDisplaywhenLargeScaleis'off'('iter'isvalidwhenLargeScaleis'on').[X,FVAL]=LINPROG(f,A,b)returnsthevalueoftheobjectivefunctionatX:FVAL=f'*X.[X,FVAL,EXITFLAG]=LINPROG(f,A,b)returnsanEXITFLAGthatdescribestheexitconditionofLINPROG.PossiblevaluesofEXITFLAGandthecorrespondingexitconditionsare1LINPROGconvergedtoasolutionX.0Maximumnumberofiterationsreached.-2Nofeasiblepointfound.-3Problemisunbounded.-4NaNvalueencounteredduringexecutionofalgorithm.-5Bothprimalanddualproblemsareinfeasible.-7Searchdirectionbecametoosmall;nofurtherprogresscanbemade.[X,FVAL,EXITFLAG,OUTPUT]=LINPROG(f,A,b)returnsastructureOUTPUTwiththenumberofiterationstakeninOUTPUT.iterations,thetypeofalgorithmusedinOUTPUT.algorithm,thenumberofconjugategradientiterations(ifused)inOUTPUT.cgiterations,andtheexitmessageinOUTPUT.message.[X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=LINPROG(f,A,b)returnsthesetofLagrangianmultipliersLAMBDA,atthesolution:LAMBDA.ineqlinforthelinearinequalitiesA,LAMBDA.eqlinforthelinearequalitiesAeq,LAMBDA.lowerforLB,andLAMBDA.upperforUB.>>A=1A=1>>A=[1321]A=1321>>A=[13;21]A=1321>>B=[12;9]B=129>>f=[-2-3]f=-2-3>>X=LINPROG(f,A,B)Warning:FunctioncallLINPROGinvokesinexactmatchD:\matlab7\toolbox\optim\linprog.m.Optimizationterminated.X=3.00003.0000>>[A,B,C]=LINPROG(f,A,B)Optimizationterminated.A=3.00003.0000B=-15.0000C=1>>a=[1100095009000000000;000800068006000000;000000140001200010000]a=Columns1through711000950090000000000800068006000000000014000Columns8through900001200010000>>a=-aa=Columns1through7-11000-9500-90000000000-8000-6800-60000000000-14000Columns8through90000-12000-10000>>b=[190000;130000;350000]b=190000130000350000>>b=-bb=-190000-13000